Fundamentals of Electric Circuits

Charles K. Alexander, Matthew N.O. Sadiku

Chapter 1

Basic Concepts - all with Video Answers

Educators

Chapter Questions

Problem 1

How many coulombs are represented by these amounts of electrons:
(a) $6.482 \times 10^{17}$
(b) $1.24 \times 10^{18}$
(c) $2.46 \times 10^{19}$
(d) $1.628 \times 10^{20}$

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Problem 2

Find the current flowing through an element if the charge flow is given by:
(a) $q(t)=(t+2) \mathrm{mC}$
(b) $q(t)=\left(5 t^{2}+4 t-3\right) \mathrm{C}$
(c) $q(t)=10 e^{-4 t} \mathrm{pC}$
(d) $q(t)=20 \cos 50 \pi t \mathrm{nC}$
(e) $q(t)=5 e^{-2 t} \sin 100 t \mu \mathrm{C}$

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Problem 3

Find the charge $q(t)$ flowing through a device if the current is:
(a) $i(t)=3 \mathrm{A}, q(0)=1 \mathrm{C}$
(b) $i(t)=(2 t+5) \mathrm{mA}, q(0)=0$
(c) $i(t)=20 \cos (10 t+\pi / 6) \mu \mathrm{A}, q(0)=2 \mu \mathrm{C}$
(d) $i(t)=10 e^{-30 t} \sin 40 t$ A, $q(0)=0$

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Problem 4

The current flowing through a device is $i(t)=5 \sin 6 \pi t$ A. Calculate the total charge flow through the device from $t=0$ to $t=10 \mathrm{ms}$

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Problem 5

Determine the total charge flowing into an element for $0<t<2$ s when the current entering its positive terminal is $i(t)=e^{-2 t} \mathrm{mA}$

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Problem 6

The charge entering a certain element is shown in Fig. $1.20 .$ Find the current at:
(a) $t=1 \mathrm{ms}$
(b) $t=6 \mathrm{ms}$
(c) $t=10 \mathrm{ms}$

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Problem 7

The charge flowing in a wire is plotted in Fig. 1.21 Sketch the corresponding current.

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Problem 8

The current flowing past a point in a device is shown in Fig. $1.22 .$ Calculate the total charge through the point.

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Problem 9

The current through an element is shown in Fig. 1.23. Determine the total charge that passed through the element at:
(a) $t=1 \mathrm{s}$
(b) $t=3 \mathrm{s}$
(c) $t=5 \mathrm{s}$

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Problem 10

A certain electrical element draws the current $i(t)=10 \cos 4 t \mathrm{A}$ at a voltage $v(t)=120 \cos 4 t \mathrm{V}$ Find the energy absorbed by the element in 2 s.

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Problem 11

The voltage $v$ across a device and the current $i$ through it are
\[v(t)=5 \cos 2 t \mathrm{V}, \quad i(t)=10\left(1-e^{-0.5 t}\right) \mathrm{A}\]
Calculate:
(a) the total charge in the device at $t=1$ s
(b) the power consumed by the device at $t=1$ s.

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Problem 12

The current entering the positive terminal of a device is $i(t)=3 e^{-2 t}$ A and the voltage across the device is $v(t)=5 d i / d t$ V.
(a) Find the charge delivered to the device between $t=0$ and $t=2 \mathrm{s}$
(b) Calculate the power absorbed.
(c) Determine the energy absorbed in 3 s.

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Problem 13

Figure 1.24 shows the current through and the voltage across a device. Find the total energy absorbed by the device for the period of $0<t<4$ s.

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Problem 14

Figure 1.25 shows a circuit with five elements. If $p_{1}=-205 \mathrm{W}, p_{2}=60 \mathrm{W}, p_{4}=45 \mathrm{W}, p_{5}=30 \mathrm{W}$
calculate the power $p_{3}$ received or delivered by element 3

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Problem 15

Find the power absorbed by each of the elements in Fig. 1.26

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Problem 16

Determine $I_{o}$ in the circuit of Fig. 1.27

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Problem 17

Find $V_{o}$ in the circuit of Fig. 1.28

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Problem 18

It takes eight photons to strike the surface of a photodetector in order to emit one electron. If $4 \times 10^{11}$ photons/second strike the surface of the photodetector, calculate the amount of current flow.

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Problem 19

Find the power rating of the following electrical appliances in your household:
(a) Lightbulb
(b) Radio set
(c) TV set
(d) Refrigerator
(e) Personal computer
(f) PC printer
(g) Microwave oven
(h) Blender

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Problem 20

A $1.5-\mathrm{kW}$ electric heater is connected to a $120-\mathrm{V}$
source.
(a) How much current does the heater draw?
(b) If the heater is on for 45 minutes, how much energy is consumed in kilowatt-hours (kWh)?
(c) Calculate the cost of operating the heater for 45 minutes if energy costs 10 cents/kWh.

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Problem 21

A $1.2-\mathrm{kW}$ toaster takes roughly 4 minutes to heat four slices of bread. Find the cost of operating the toaster once per day for 1 month $(30$ days). Assume energy costs 9 cents/kWh.

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Problem 22

A flashlight battery has a rating of 0.8 ampere-hours
(Ah) and a lifetime of 10 hours.
(a) How much current can it deliver?
(b) How much power can it give if its terminal voltage is $6 \mathrm{V} ?$
(c) How much energy is stored in the battery in kWh?

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Problem 23

A constant current of 3 A for 4 hours is required to charge an automotive battery. If the terminal voltage is $10+t / 2 \mathrm{V}$, where $t$ is in hours,
(a) how much charge is transported as a result of the charging?
(b) how much energy is expended?
(c) how much does the charging cost? Assume electricity costs 9 cents/kWh.

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Problem 24

A $30-\mathrm{W}$ incandescent lamp is connected to a $120-\mathrm{V}$ source and is left burning continuously in an otherwise dark staircase. Determine:
(a) the current through the lamp,
(b) the cost of operating the light for one non-leap year if electricity costs 12 cents per $\mathrm{kWh}$.

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Problem 25

An electric stove with four burners and an oven is used in preparing a meal as follows.
Burner 1: 20 minutes $\quad$ Burner 2: 40 minutes
Burner 3: 15 minutes Burner 4: 45 minutes
Oven: 30 minutes If each burner is rated at $1.2 \mathrm{kW}$ and the oven at $1.8 \mathrm{kW},$ and electricity costs 12 cents per $\mathrm{kWh}$ calculate the cost of electricity used in preparing the meal.

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Problem 26

PECO (the electric power company in Philadelphia) charged a consumer $\$ 34.24$ one month for using $215 \mathrm{kWh}$. If the basic service charge is $\$ 5.10$, how much did PECO charge per kWh?

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Problem 27

A telephone wire has a current of $20 \mu$ A flowing through it. How long does it take for a charge of $15 \mathrm{C}$ to pass through the wire?

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Problem 28

A lightning bolt carried a current of $2 \mathrm{kA}$ and lasted for $3 \mathrm{ms}$. How many coulombs of charge were contained in the lightning bolt?

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Problem 29

The power consumption for a certain household for a day is shown in Fig. $1.29 .$ Determine:
(a) the total energy consumed in $\mathrm{kWh}$
(b) the average power per hour.

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Problem 30

The graph in Fig. 1.30 represents the power drawn by an industrial plant between 8: 00 and 8: 30 A.M.
Calculate the total energy in MWh consumed by the plant.

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Problem 31

A battery may be rated in ampere-hours (Ah). An lead-acid battery is rated at 160 Ah.
(a) What is the maximum current it can supply for $40 \mathrm{h} ?$
(b) How many days will it last if it is discharged at $1 \mathrm{mA} ?$

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Problem 32

How much work is done by a $12-\mathrm{V}$ automobile battery in moving $5 \times 10^{20}$ electrons from the positive terminal to the negative terminal?

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Problem 33

How much energy does a 10 -hp motor deliver in 30 minutes? Assume that 1 horsepower $=746 \mathrm{W}$

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Problem 34

A $2-\mathrm{kW}$ electric iron is connected to a $120-\mathrm{V}$ line. Calculate the current drawn by the iron.

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